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Pair of Lines Passing Though Origin

The positive ...

Question

The positive value of parameter ' $a$ ' for which the area bounded by parabolas $y = x - a x^{2}$ & $a y = x^{2}$ attains its the maximum value is

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Solution

On solving, we get $x = 0, \frac{a}{a^{2} + 1}$
Required area $= \int_{0}^{λ / 1 + λ^{2}} (x - a x^{2} - \frac{x^{2}}{a}) d x$
$Δ^{'} = \frac{a (1 - a) (1 + a)}{(1 + a^{2})^{3}}$
$\Rightarrow a = 1$ gives maximum.

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Pair of Lines Passing Though Origin

Standard XII Mathematics

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